Applications of the Method of Differential Inequalities in Singular Perturbation Problems

Abstract

Publisher Summary The maximum principle, a very important special case of the method of differential inequalities, is well known for its applicability in singular perturbation problems. The technique of differential inequalities is been effectively utilized to give an elegant, unified and comprehensive treatment of some classical singular perturbed nonlinear second order boundary value problems. The chapter illustrates the versitility and applicability of differential inequalities in singular perturbation problems by studying the model nonlinear singular perturbation problem whose solutions exhibit a wide variety of interesting behavior. But, one or more solutions of the reduced problem may be required to approximate the solution y, and the transition may occur in an interior boundary (shock) layer. The chapter discusses the principle existence and comparison theorem, the model problem, Nagumo theorem, and various theorems.